Optical isolator based on the electro-optic effect in periodically poled lithium niobate with the addition of a half domain

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1 Optical isolator based on the electro-optic effect in periodically poled lithium niobate with the addition of a half domain Lei Shi, Linghao Tian, and Xianfeng Chen* Department of Physics, The State Key Laboratory on Fiber Optic Local Area Communication Networks and Advanced Optical Communication Systems, Shanghai Jiao Tong University, 800 Dongchuan Rd., Shanghai , China *Corresponding author: xfchen@sjtu.edu.cn Received 15 October 2012; revised 10 November 2012; accepted 16 November 2012; posted 16 November 2012 (Doc. ID ); published 13 December 2012 We propose an optical isolator based on the electro-optic (EO) effect of periodically poled lithium niobate (PPLN). When the EO effect occurs in PPLN under a TE field, each domain serves as a half-wave plate under the quasi-phase-matching condition, and PPLN shows optical activity similar to quartz. The introduction of an additional half-domain to the normal PPLN changes the incident azimuth angle of the reflected light. As a result, the reflected light does not return to the original polarization state. Thus, the optical rotation accumulates and optical isolation occurs. The isolator can be employed for all linearly polarized light and has the advantage of being used in a weak-light system with low driving voltage and high isolation contrast Optical Society of America OCIS codes: , Introduction Optical signal isolation requires time-reversal symmetry breaking. In bulk optics, this is achieved by using materials that exhibit the magneto-optic effect via the Faraday effect. For these materials, optical rotation accumulates for light traveling back and forth in the medium, based on the fact that light rotates in the reverse sense during the forward and backward pass. In this manner, the Faraday effect has long served as a routine principle for achieving optical isolation [1 4]. With increased demand for nonmagnetic optical isolation, various alternative mechanisms have been proposed, such as the use of graded dissipative media, left-handed periodic structures with a Kerr nonlinear defect layer, and dynamic photonic materials that allow photonic transitions [5 13]. In recent decades, considerable attention has been paid to photonic crystals [14 19] X/12/ $15.00/ Optical Society of America and nonlinear optical processes [20,21]. In these systems, however, optical isolation is available only in specific power ranges [20,21]. In addition, research has been aimed at achieving optical isolation in reciprocal structures that have no inversion symmetry, e.g., chiral structures. In these cases, however, apparent isolation occurs only for a restricted photon state in the backward pass and not for an arbitrary backward incident state. On the other hand, in addition to the Faraday media, there exist numerous optically active materials, such as quartz and periodically poled lithium niobate (PPLN) [22], where optical rotation of light can occur, but not optical isolation. This is because in these materials light rotates in the same sense in the forward and backward pass, and therefore there is no optical rotation accumulation after a round trip through the medium. In this paper, we propose an optical isolator based on the electro-optic (EO) effect of PPLN, a newly discovered optically active material. By introducing an additional half-domain that acts as a quarter-wave plate to the normal PPLN, the incident azimuth 20 December 2012 / Vol. 51, No. 36 / APPLIED OPTICS 8521

2 angle of the reflected light can be changed, and therefore the light does not return to the original polarization state, as it does not follow the same reverse path. In this manner, optical rotation accumulates, which induces optical isolation. The isolator proposed here can be employed for all linearly polarized light and has the advantage of being used in a weak-light system with low driving voltage. In theory, the isolation contrast in this system can reach unity. 2. Theoretical Analysis The Faraday effect originates from the difference in speeds of the left and right circularly polarized light propagating in optically transparent dielectric materials under the influence of a magnetic field, a property known as circular birefringence. In the Faraday effect, the polarization plane of linearly polarized light rotates around the direction of motion as light travels through a Faraday medium. However, unlike the case of an optically active medium, the polarized light reflected back through the same Faraday medium does not undo the same polarization change it underwent in its forward pass. If left rotation occurs in the forward pass, right rotation occurs in the backward pass, and vice versa. In other words, the Faraday effect is a nonreciprocal process. As a result, the polarization rotation doubles in a round trip through the medium, and thus optical rotation accumulates due to the different chirality in the different directions. For optically active materials, the chirality is the same for the forward and backward passes. Thus the light returns to its original state after passing back and forth through the medium, not contributing to the optical isolation. Thus far, no technique for providing optical isolation using optically active materials has been developed. However, if the incident azimuth angle of the reflected light is changed, the reflected light does not undergo the forward rotation change, and consequently does not return to the incident state. By suitably controlling the incident angle of the reflected light, the polarization state at the output can be made perpendicular to that of the forward incident light, making optical isolation possible. We are now attempting to realize optical isolation in PPLN based on this concept. PPLN is a typical quasi-phase-matching (QPM) material with nonlinear coefficients, such as the EO coefficient, the acousto-optic coefficient, and the piezo-electric coefficient, varying periodically due to the periodic domain inversion. In 2000, Lu et al. [23] proposed the optical rotation in PPLN based on the EO effect. When a TE field is applied to PPLN, the refractive index ellipsoid is deformed. As a result, the optical axes of each domain are alternately aligned at an angle of θ or θ with respect to the original axes. The rocking angle θ is given by θ γ 51 E 1 n e 2 1 n o 2 ; (1) where γ 51 is the EO coefficient, E is the electric field intensity, and n o and n e are refractive indices of the ordinary and extraordinary waves, respectively. The coupled-wave equations of the ordinary and extraordinary waves in PPLN are dao dx iκa e e iδβx da e dx iκ A o e iδβx ; 2 with Δβ k o k e m 2π Λ. Λ is the period of the PPLN and κ ω 2c n2 on 2 p e γ 51 E n o n e i 1 cos mπ mπ m 1; 3; 5. A o and A e are the normalized complex amplitude of the ordinary and extraordinary waves, respectively. Under the QPM condition (Δβ 0), solutions of the coupled-wave equations are given by [24] Ao L cos jκjl A o 0 sin jκjl A e 0 A e L cos jκjl A e 0 sin jκjl A o 0 : 3 For the coherence length L c λ 2 n o n e, the QPM condition is satisfied for a given wavelength λ if each domain thickness is equal to L c or its multiple. For a PPLN with the domain thickness of L c, jκjl c 2θ, each domain serves as a half-wave plate with respect to the input light. After passing through N periods of the domain, the polarization plane of the incident light rotates by an angle of 4Nθ. We experimentally verified the optical rotation of light in the PPLN by the EO effect (Fig. 1); the details of the experimental setup are given in [25,26]. The discrepancy between the theoretical and experimental result may arise from the temperature fluctuation and deviation between the theoretical and practical refractive indices of PPLN. However, the primary reason for the discrepancy may be the presence of a finite gap between the electrode and the PPLN Fig. 1. (Color online) Experimental verification of the optical rotation in PPLN by the EO effect. The input wavelength of light is 1542 nm, and the experiment was conducted at a temperature of 20 C. The PPLN used in our experiment is MgO doped and 3.6 cm long. The period of the domain structure is 19.7 μm, with a duty cycle of APPLIED OPTICS / Vol. 51, No. 36 / 20 December 2012

3 additional domain with half the domain thickness is introduced, optical rotation may be achieved [28]. Fig. 2. (Color online) Polarization evolution process of light in HPPLN. Y and Z represent the principal axes of the index ellipsoid, and P represents the polarization state of light. The incident light satisfies the QPM condition. Fig. 3. (Color online) Schematic diagram of the optical isolator based on the EO effect of HPPLN. A positive half-domain is added to the normal PPLN to form HPPLN. Under the QPM condition, each domain serves as a half-wave plate, and the half-domain serves as a quarter-wave plate. sample [25]. The nonzero rotation at E 0 is caused by the strain-optic effect [27], which causes a rocking angle between the optical axes of the positive and negative domains, even without an electric field. In our previous study, we showed that optical propagation is reciprocal in PPLN by the EO effect, which bears similarity to natural optical activity [22]. Light rotates in the same sense during the forward and backward pass in PPLN, and optical rotation accumulates little for the reflected light, not contributing to optical isolation. However, if an 3. Results and Discussion A domain with half the domain thickness is equivalent to a quarter-wave plate in the same manner that a complete domain is equivalent to a half-wave plate. Linearly polarized light becomes circularly polarized after passing through a quarter-wave plate, and vice versa. Meanwhile, light passing through a quarterwave plate twice has the same effect as that of light passing through a half-wave plate once. Thus, an additional domain with half the domain thickness is added to the normal PPLN (the positive and negative domains appear as a pair); this newly formed PPLN with an additional half-domain is henceforth referred to as HPPLN. As a result, the polarization direction of the reflected light, incident on the PPLN in the backward pass, has changed by the time it is transmitted out of the PPLN in the forward pass. Optical rotation is therefore accumulated. Figure 2 shows a detailed description of the polarization evolution process of light in HPPLN. Specifically, when the electric field is applied along the -Y axis, for incident light with an azimuth angle of y o xθ, the light undergoes right rotation in the forward pass; the azimuth angle, after passing through N periods, is y in 4N x θ. The light becomes circularly polarized after the half-domain and transmits out. On the other hand, the reflected light becomes linearly polarized with an azimuth angle of 4N x 2 θ after the half-domain. It then undergoes right rotation and transmits out with an azimuth angle of y ref 8N x 2 θ. The angle between the reflected and incident light can be easily calculated as jy ref j jy in j 4Nθ 2θ. According to Eq. (1), under a suitable electric field, it is easy to make the reflected light perpendicular to the incident light, i.e., jy ref j jy in j 4Nθ 2θ π 2 ; 3π 2. The reflected light is thus blocked. Figure 3 gives the schematic diagram of the optical isolator based on the EO effect of HPPLN. Interestingly, the angle between the reflected and incident light Fig. 4. (Color online) (a) Theoretical transmittance of the incident light (solid curve) and reflected light (dashed curve) and (b) isolation contrast as a function of the external electric field. The QPM wavelength is 1550 nm. 20 December 2012 / Vol. 51, No. 36 / APPLIED OPTICS 8523

4 jy ref j jy in j is independent of the incident azimuth angle y o xθ, which implies that the isolation effect is independent of the incident azimuth angle. Thus, the isolator can be employed for all linearly polarized light. For Z polarized light, the transmittance of the incident and reflected light along the Z axis is T in cos 2 4Nθ and T ref cos 2 8Nθ 2θ [29], respectively. For an HPPLN that consists of 3650 domains, transmittance of the incident and reflected light at room temperature can be calculated as a function of the external electric field, as shown in Fig. 4(a). It is obvious that under a suitable electric field, such as E 0.5 kv cm or E 1.5 kv cm, the transmittance of the reflected light can be zero, i.e., a total block of the reflected light. To provide a straightforward view of the isolation effect, we define the isolation contrast as C T in T ref T in T ref. Figure 4(b) shows the contrast ratio versus the external electric field. The contrast ratio is smoothly tuned from 1 to 1, with the increment of the electric field, and is equal to 1 under a suitable electric field where complete optical isolation occurs. In contrast to the early attempts to realize nonmagnetic isolators based on material nonlinearity, where isolation is only achievable for strong optical intensity [20,21] or restricted polarization states (for example, in chiral structures), the optical rotation studied here depends on the electric field; the transition effect does not depend on the amplitude or phase of the incident light. By properly controlling the external electric field, it can be used in a weak-light system. In the waveguide configuration, the width of the HPPLN can be as small as 10 μm, so that 1 volt is enough to make the polarization plane rotate by 45, which is very attractive. 4. Conclusion In summary, we proposed an optical isolator based on the EO effect of PPLN. By adding a quarter-wave plate-like half-domain to the normal PPLN, optical rotation is accumulated due to the change of the incident azimuth angle of the reflected light. The isolator proposed here provides high isolation contrast in a weak-light system with low driving voltage and can be employed for all linearly polarized light. However, there are still substantial challenges that need to be overcome for the achievement of nonmagnetic optical isolators based on the EO effect of PPLN. For example, the isolator does not work for circularly or elliptically polarized light. In addition, some issues may have to be considered before realizing it in integrated optics. But it is conceivable that all these issues are addressable with the proper design of the structure of the domains and improved experimental techniques. This work was supported by the National Natural Science Foundation of China (Grant Nos , ), the National Basic Research Program 973 of China (Grant No. 2011CB808101), the Foundation for Development of Science and Technology of Shanghai (Grant No. 11XD ), and the Open Fund of the State Key Laboratory of High Field Laser Physics. References 1. J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, Waveguide optical isolator based on Mach-Zehnder interferometer, Appl. Phys. Lett. 76, (2000). 2. N. Kono, K. Kakihara, K. Saitoh, and M. Koshiba, Nonreciprocal microresonators for the miniaturization of optical waveguide isolators, Opt. Express 15, (2007). 3. Z. Yu, Z. Wang, and S. Fan, One-way total reflection with onedimensional magneto-optical photonic crystals, Appl. Phys. Lett. 90, (2007). 4. T. Amemiya, H. Shimizu, M. Yokoyama, P. N. Hai, M. Tanaka, and Y. 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